Which of the following bank accounts has the highest effective annual return?
A) an account that pays 8% nominal interest with daily (365-day) compounding.
B) an account that pays 8% nominal interest with monthly compounding.
C) an account that pays 8% nominal interest with annual compounding.
D) an account that pays 7% nominal interest with daily (365-day) compounding.
E) an account that pays 7% nominal interest with monthly compounding.

Question

Quizplus · Accepted Answer

By inspection, we can see that a dominates b and c, and that d dominates e because, with the same interest rate, the account with the most frequent compounding has the highest EFF%. Thus, the correct answer must be either a or d. Moreover, we can see by inspection that since a and d have the same compounding frequency yet a has the higher nominal rate, a must have the higher EFF%. You could also prove that a is the correct choice by calculating the EFF%s:
 a. $ \quad 8.328 \%=(1+0.08 / 365)^{365-1} $
b. $ \quad 8.300 \%=(1+0.08 / 12)^{12-1} $
c. $ \quad8.000 \%=(1+0.08 / 1)^{1-1} $
d. $ \quad 7.250 \%=(1+0.07 / 365)^{365-1} $
e. $ \quad7.229 \%=(1+0.07 / 12)^{12-1} $

Which of the Following Bank Accounts Has the Highest Effective